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Showing posts from May, 2009

Frequently misunderstood logic: modus tollens

Back when I was in upper school I studied Further Mathematics and one of the topics I loved was logic. We learnt about syllogism and modus ponens, and my favorite modus tollens.

Modus tollens is fun because it is often applied incorrectly in informal arguments to come to the wrong conclusion. Here's an example.

The other day I saw a tweet which read:

"A fear of weapons is a sign of retarded sexual and emotional maturity." - Sigmund Freud, General Introduction to Psychoanalysis (1952)

Simplifying that a little (and assuming we agree with Freud) it can be written "If a person is fearful of weapons, then that person is sexually and emotionally immature". If we write "fearful of weapons" as F and "sexually and emotionally immature" as I, this statement can be rewritten F => I (the => is read as implies and make the entire statement read as F implies I or If F, then I).

So if we come across someone who satisfies F (i.e. they fear weapons) the…